Exact Ω₂ Identities for S4,2(x) with Amortized Performance Gains

This archive contains complete reproducibility materials for "Exact Ω₂ Identities for S4,2(x) with Amortized Performance Gains" submitted to Experimental Mathematics. We present exact closed-form identities for the weight-6 Euler sum S₄,₂(x) = Σ(Hₙ₋₁xⁿ/n⁵) at dyadic arguments x ∈ {1/2, 1/4, -1/2} in a canonical Ω₂ constant field. Using PSLQ at 300+ digit precision, we discover that S₄,₂(x) admits exact representation as rational linear combinations of 21 basis constants. The identities are certified by independent high-precision residual verification (errors < 10⁻⁹⁵). We establish first-principles derivation via harmonic polylogarithm theory and demonstrate amortized computational advantages.